scholarly journals On the Quadratic Finite Element Approximation of One-Dimensional Waves: Propagation, Observation, and Control

2012 ◽  
Vol 50 (5) ◽  
pp. 2744-2777 ◽  
Author(s):  
Aurora Marica ◽  
Enrique Zuazua
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
One Dimensional ◽  
Waves Propagation ◽  
And Control

DISCRETE COMPACTNESS FOR p AND hp 2D EDGE FINITE ELEMENTS

2003 ◽  
Vol 13 (11) ◽  
pp. 1673-1687 ◽  
Author(s):  
DANIELE BOFFI ◽  
LESZEK DEMKOWICZ ◽  
MARTIN COSTABEL
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Stability Estimate ◽  
Element Approximation ◽  
Dimensional Model ◽  
Compactness Property ◽  
One Dimensional ◽  
Discrete Compactness

In this paper we discuss the hp edge finite element approximation of the Maxwell cavity eigenproblem. We address the main arguments for the proof of the discrete compactness property. The proof is based on a conjectured L2 stability estimate for the involved polynomial spaces which has been verified numerically for p≤15 and illustrated with the corresponding one dimensional model problem.

A Nonconforming Finite Element Approximation for Optimal Control of an Obstacle Problem

2016 ◽  
Vol 16 (4) ◽  
pp. 653-666 ◽  
Author(s):  
Asha K. Dond ◽  
Thirupathi Gudi ◽  
Neela Nataraj
Keyword(s):  
Finite Element ◽  
Optimization Problems ◽  
Finite Element Approximation ◽  
The State ◽  
Element Approximation ◽  
Nonconforming Finite Element ◽  
Nonconforming Finite Elements ◽  
Adjoint Variables ◽  
Variational Discretization ◽  
And Control

AbstractThe article deals with the analysis of a nonconforming finite element method for the discretization of optimization problems governed by variational inequalities. The state and adjoint variables are discretized using Crouzeix–Raviart nonconforming finite elements, and the control is discretized using a variational discretization approach. Error estimates have been established for the state and control variables. The results of numerical experiments are presented.

A one-dimensional quasi-static contact problem in linear thermoelasticity

1993 ◽  
Vol 4 (2) ◽  
pp. 151-174 ◽  
Author(s):  
M. I. M. Copetti ◽  
C. M. Elliott
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Numerical Experiments ◽  
Finite Element Approximation ◽  
Unilateral Contact ◽  
Element Approximation ◽  
Time Step ◽  
One Dimensional ◽  
Static Contact ◽  
Linear Thermoelasticity

The existence, uniqueness and regularity of the solution to a one-dimensional linear thermoelastic problem with unilateral contact of the Signorini type are established. A finite element approximation is described, and an error bound is derived. It is shown that if the time step is O(h2), then the error in L2 in the temperature and in L∞ in the displacement is O(h). Some numerical experiments are presented.

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